Photo of Alastair Craw

Alastair Craw

Dr

  • 4 WEST 3.49

Accepting Doctoral Students

If you made any changes in Pure these will be visible here soon.

Personal profile

Research interests

My research interests lie in pure mathematics, and specifically in algebraic geometry and representation theory. Much of my research applies explicit methods to improve our understanding of moduli spaces of quiver representations and their derived categories.

One motivating question is to ask for nice moduli descriptions of well known varieties. This is now understood for projective toric varieties and, more generally, for Mori Dream Spaces. This leads naturally to the study of multigraded linear series (also known as framed quiver varieties or quiver flag varieties) as ambient spaces in noncommutative algebraic geometry.Another theme of my research is to understand which algebraic varieties carry tilting bundles, thereby providing an explicit understanding of their derived category of coherent sheaves. The first known examples were provided by Beilinson and Kapranov, while many of the more recent examples have been influenced by the McKay correspondence in one form or another. Examples include framed quiver varieties, G-Hilbert schemes, moduli spaces arising in the study of consistent dimer model algebras, and smooth toric Fano varieties in low dimensions. These constructions lead to interesting questions about mutation, wall crossing phenomena and Bridgeland stability manifolds.

Education/Academic qualification

Mathematics, Doctor of Science, University of Warwick

Award Date: 12 Jul 2001

Fingerprint

Dive into the research topics where Alastair Craw is active. These topic labels come from the works of this person. Together they form a unique fingerprint.
  • 2 Similar Profiles

Network

Recent external collaboration on country level. Dive into details by clicking on the dots or
If you made any changes in Pure these will be visible here soon.